<PAGE>

THIS WARRANT AND THE RIGHTS REPRESENTED HEREBY SHALL NOT BE TRANSFERABLE AT ANY
TIME UNLESS (I) A REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933, AS
AMENDED, SHALL BE IN EFFECT WITH RESPECT TO THIS WARRANT OR THE SHARES ISSUABLE
HEREUNDER AT SUCH TIME, OR (II) THE TRANSFER IS MADE IN COMPLIANCE WITH THE
PROVISIONS OF SECTION 5.

NUMBER:                                                            25,000 SHARES

                                    WARRANT
                              TO PURCHASE SHARES
                                      OF
                             TIPPERARY CORPORATION


     This certifies that, for value received, Richard A. Barber, an individual
residing in Brisbane, Queensland, Australia ("Barber"), or his registered
assigns, is entitled to purchase from TIPPERARY CORPORATION, a Texas corporation
(the "Company"), twenty-five thousand (25,000) Shares, at the price of One
Dollar and 65/100 ($1.65) U.S. per Share (as defined in Section 3) at any time,
or in part from time to time in accordance with the following Vesting Schedule
("Vesting Schedule"):

     Date:                                Total Shares Subject to Exercise

From and after January 1, 2003                           8,333
From and after January 1, 2004                          16,666
From and after January 1, 2005                          25,000

This Warrant shall expire, if not exercised prior thereto, two (2) years after
the resignation or removal of Barber as a consultant of the Company.  If Barber
should resign or be removed as a consultant from the Company, then this Warrant
shall be vested only to the extent vested on such date of resignation or removal
according to the Vesting Schedule.  The provisions as to adjustment of the
initial exercise price set forth above and the number of Shares to be issued
upon the occurrence of certain events (the Provisions as to Adjustment) are more
fully set forth in Annex I hereto.  (Hereinafter, the initial exercise price set
forth above in this paragraph for the purchase of Shares upon the exercise of
this Warrant, as adjusted pursuant to the Provisions as to Adjustment, is
referred to as the "Exercise Price").  This Warrant is subject to the following
provision, terms and conditions:

     1.  EXERCISE OF WARRANT.

     (a) The rights represented by this Warrant may be exercised by the holder
hereof, in whole or in part, (but not as to a fractional Share), by the
surrender of this Warrant at the Company's principal office located in Denver,
Colorado (or such other office or agency of the Company as the Company may
designate by notice in writing to the holder hereof at the address of such
holder appearing on the books of the Company at any time within the period above
named) and delivery of a

Page 1 - Warrant to Purchase Shares
<PAGE>

completed subscription form in the form attached to this Warrant as Exhibit A,
and upon payment to the Company of the Exercise Price for such Shares.

     (b) Payment of the Exercise Price shall be made by a combination of any one
or more of the following:

          (i)  By application, to the extent permitted by applicable law, of
               Shares or other securities of the Company owned by the holder
               hereof, the value of which for such purpose shall be the fair
               market value thereof determined in good faith by the Company and
               the holder hereof at the time of such exercise; provided,
               however, that in order to apply such Shares or other securities
               of the Company in the exercise hereof, each of the following
               conditions must be met:

               (A)  Such Shares or other securities of the Company shall have
                    been owned, without material encumbrance, contingency or
                    risk of forfeiture relating to the ownership rights, for at
                    least six months and at all times during said six month
                    period by the holder hereof, and within said six month
                    period such Shares or other securities of the Company shall
                    not have been obtained through exercise of any option,
                    warrant or right to obtain such Shares of other securities
                    or through the conversion of any other security; and

               (B)  Such Shares or other securities shall not be or include: (1)
                    options, warrants or similar rights to acquire Shares or
                    other securities of the Company by the holder hereof; or (2)
                    securities owned by the holder hereof which are convertible
                    in whole or in part into Shares or other securities of the
                    Company.

          (ii) in cash or by certified check or bank draft in New York Clearing
               House funds.

     (c) The Company agrees that any Shares so purchased by the exercise of this
Warrant shall be deemed to be issued to the holder hereof as the record owner of
such Shares as of the close of business on the date on which this Warrant shall
have been surrendered, the completed subscription form delivered, and payment in
full is made and delivered to the Company for such Shares as aforesaid.

     (d) Stock certificates evidencing Shares so purchased shall be delivered to
the holder hereof as promptly as practicable, after the rights represented by
this Warrant shall have been so exercised.  If this Warrant shall have been
exercised only in part, and unless this Warrant has expired, a new Warrant
representing the number of Shares with respect to which this Warrant shall

Page 2 - Warrant to Purchase Shares
<PAGE>

not then have been exercised shall also be delivered to the holder hereof within
such time. Notwithstanding the foregoing, however, the Company shall not be
required to deliver any stock certificate evidencing Shares upon exercise of
this Warrant except in accordance with the provisions, and subject to the
limitations, of Section 5. The Company will pay all expenses and charges payable
in connection with the preparation, execution and delivery of stock certificates
and any new Warrants or promissory notes.

     2.  CERTAIN COVENANTS OF THE COMPANY.  The Company covenants and agrees as
follows:

     (a) All Shares which may be issued upon the exercise of the rights
represented by this Warrant (all such Shares, whether previously issued or
subject to issuance upon the exercise of this Warrant, are from time to time
referred to herein as "Warrant Shares") will, upon issuance, be duly authorized
and issued, fully paid and nonassessable and free from all taxes, liens and
charges with respect to the issuance thereof.

     (b) During the period within which the rights represented by this Warrant
may be exercised, and only insofar as the Vesting Schedule herein permits the
exercise of this Warrant, the Company will at all times have authorized and
reserved free of preemptive or other rights for the exclusive purpose of
issuance upon exercise of the purchase rights evidenced by this Warrant, a
sufficient number of Shares to provide for the exercise of rights represented by
this Warrant.

     (c) The Company will not, by amendment or restatement of the Articles of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, issuance or sale of securities or otherwise, avoid or take any action
which would have the effect of avoiding the performance of any of the terms to
be performed hereunder by the Company, but will at all times in good faith carry
out all of the provisions of this Warrant and take all such action as may be
necessary or appropriate to protect the rights of the holder hereof against
dilution or other impairment and, in particular, will not permit the par value
of any Share to be or become greater than the then effective Exercise Price.

     3.  DEFINITION OF SHARES.  As used herein, the term "Shares" shall mean and
include shares of the Common Stock, par value $.02 U.S. per share, of the
Company as are constituted and exist on the date hereof, and shall also include
any other class of the capital stock of the Company hereafter authorized which
shall neither be limited to a fixed sum or percentage of par value in respect to
the rights of the holders thereof to receive dividends and to participate in the
distribution of assets upon the voluntary or involuntary liquidation,
dissolution or winding up of the Company, nor be subject at any time to
redemption by the Company; provided that the Shares receivable upon exercise of
this Warrant shall include only Shares of the type as are constituted and exist
on the date hereof or Shares resulting from any reclassification of the Shares
as provided for in paragraph (C) of the Provisions as to Adjustment.

Page 3 - Warrant to Purchase Shares
<PAGE>

     4.  NO RIGHTS OR LIABILITIES AS A SHAREHOLDER.  This Warrant shall not
entitle the holder hereof as such to any rights whatsoever, including, without
limitation, voting rights, as a holder of Shares of the Company.  No provisions
hereof, in the absence of affirmative action by the holder hereof to purchase
Shares, and no mere enumeration herein of the rights or privileges of such
holder, shall give rise to any liability of such holder as a holder of Shares of
the Company, regardless of who may assert such liability.

     5.  RESTRICTIONS ON TRANSFER.

     (a) This Warrant shall not be exercisable by a transferee hereof and/or
transferable and the Warrant Shares shall not be transferable except upon the
conditions specified in this Section 5, which conditions are intended, among
other things, to ensure compliance with the provisions of the Securities Act of
1933, as amended, and the rules and regulations of the Securities and Exchange
Commission (the "Commission") thereunder (collectively the "Securities Act"), in
respect of the exercise and/or transfer of this Warrant and/or transfer of such
Warrant Shares.

     (b) This Warrant and the Warrant Shares shall not be transferable (except
for a transfer of this Warrant or the Warrant Shares in an offering registered
under the Securities Act, including, without limitation, a transfer in a
registered offering effected pursuant to Section 6, and any subsequent transfer)
unless, prior to any transfer, the holder hereof shall have received from its
transferee reasonable assurances that such person is aware that this Warrant and
the Warrant Shares have not been registered under the Securities Act and that
such person is acquiring this Warrant or the Warrant Shares for investment only
and not with the view to the disposition or public offering thereof (unless in
an offering registered under the Securities Act of 1933 or exempt therefrom),
and that such person is aware that the stock certificates evidencing the Warrant
Shares shall bear a legend restricting transfer and disposition thereof in
accordance with the Securities Act unless, in the opinion of counsel to the
Company, such legend may be omitted.  In the event of any transfer of this
Warrant (other than a transfer in an offering registered under the Securities
Act, including, without limitation, a transfer in a registered offering effected
pursuant to Section 6, and any subsequent transfer), the holder hereof shall
provide an opinion of counsel, who shall be reasonably satisfactory to the
Company, that an exemption from the registration requirements of the Securities
Act is available.

     (c) Any permitted subsequent holder of this Warrant shall be subject to all
the terms and conditions herein, and shall acknowledge, in writing, upon receipt
of this Warrant his or her acceptance of the terms and conditions herein.

     (d) To facilitate sales by a holder of this Warrant or Warrant Shares in
transactions qualifying under Rule 144 promulgated by the Commission under the
Securities Act, if available, the Company agrees to satisfy the current public
information requirements of said Rule 144, for as long as the Shares remain
registered under the Securities Exchange Act of 1934, as amended, and the rules
and regulations of the Commission thereunder (collectively the "Exchange Act"),
and to provide said holder upon request with such other information as such
holder may require for compliance with the provisions of said Rule 144.

Page 4 - Warrant to Purchase Shares
<PAGE>

     6.  REGISTRATION UNDER SECURITIES ACT.

     (a) If the Company at any time proposes to register any issuance of its
securities under the Securities Act (other than a registration on Form S-8 in
connection with an employee stock purchase or option plan or on Form S-4 in
connection with mergers, acquisitions or exchange offerings), the Company will
at such time give prompt written notice to the holder hereof and to the holders
of all other Warrant Shares issuable from any outstanding Warrants (such holders
are hereinafter referred to as the "Prospective Sellers") of its intention to do
so.  Upon the written request of a Prospective Seller, given within 30 days
after receipt of any such notice (which request shall state the intended method
of disposition of the Warrant Shares to be transferred by such Prospective
Seller), the Company shall use its best efforts to cause all Warrant Shares, the
holders of which (or of the Warrants to which the same are related), to the
extent vested in accordance with the Vesting Schedule, shall have so requested
registration of the transfer thereof, to be registered under the Securities Act,
all to the extent requisite to permit the sale or other disposition (in
accordance with the intended method thereof as aforesaid) by the Prospective
Sellers of such Warrant Shares.  The rights granted pursuant to this Section
6(a) shall not be effective with respect to the Prospective Seller in the case
of an underwritten public offering of securities of the Company by the Company
unless each Prospective Seller agrees to the terms and conditions, including
underwriting discounts and allowances, specified by the managing underwriter of
such offering with respect to such Warrant Shares.  The Company shall have the
right to reduce the number of Warrant Shares of the Prospective Sellers to be
included in a registration statement pursuant to the exercise of the rights
granted by this Section 6(a) if, and to the extent, that the managing
underwriter of such offering is of the good faith opinion, supported by written
reasons therefor, that the inclusion of such Warrant Shares would materially
adversely affect the marketing of the securities of the Company to be offered;
provided, that any such reduction of the number of Warrant Shares the transfer
of which is to be registered on behalf of the Prospective Sellers shall be made
on the basis of a pro rata reduction of all Warrant Shares of all Prospective
Sellers.

     (b) If and whenever the Company is required by the provisions of this
Section 6 to use its best efforts to effect the registration of any transfer of
Warrant Shares under the Securities Act, the Company will, as expeditiously as
possible,

          (i)  prepare and file with the Commission a registration statement
               with respect to such transfer and use its best efforts to cause
               such registration statement to become and remain effective, but
               not for any period longer than nine months;

          (ii) prepare and file with the Commission such amendments and
               supplements to such registration statement and the prospectus
               used in connection therewith as may be necessary to keep such
               registration statement effective, and to comply with the
               provisions of the Securities Act with respect to the transfer of
               all securities covered by such registration statement, including,
               without

Page 5 - Warrant to Purchase Shares
<PAGE>

                limitation, taking all necessary actions whenever the
                Prospective Sellers of the Warrant Shares covered by such
                registration statement shall desire to dispose of the same;

          (iii) furnish to each Prospective Seller such number of copies of a
                prospectus, including a preliminary prospectus, in conformity
                with the requirements of the Securities Act, and such other
                documents, as such Prospective Seller may reasonably request in
                order to facilitate the disposition of the Warrant Shares owned
                by such Prospective Seller and covered by such registration
                statement;

          (iv)  use its best efforts to register or qualify the securities
                covered by such registration statement under such other
                securities or blue sky laws of such jurisdictions as each
                Prospective Seller shall request, and use its best efforts to do
                any and all other acts and things which may be reasonably
                necessary to enable such Prospective Seller to consummate the
                disposition in such jurisdiction of the Warrant Shares owned by
                such Prospective Seller and covered by such registration
                statement; provided that, notwithstanding the foregoing, the
                Company shall not be required to register in any jurisdiction as
                a broker or dealer of securities or to grant its consent to
                service of process in any such jurisdiction solely on account of
                such intended disposition by such Prospective Seller;

          (v)   furnish to the Prospective Sellers whose intended dispositions
                are registered a signed copy of an opinion of counsel for the
                Company, in form and substance acceptable to such Prospective
                Sellers, to the effect that: (A) a registration statement
                covering such dispositions of Warrant Shares has been filed with
                the Commission under the Securities Act and has been made
                effective by order of the Commission, (B) such registration
                statement and the prospectus contained therein and any
                amendments or supplements thereto comply as to form in all
                material respects with the requirements of the Securities Act,
                and nothing has come to such counsel's attention which would
                cause him to believe that the registration statement or such
                prospectus, amendment or supplement, at the time such
                registration statement or amendment became effective or such
                supplement was filed with the Commission, contained any untrue
                statement of a material fact or omitted to state a material fact
                required to be stated therein or necessary to make the
                statements therein (in the case of such prospectus, amendment or
                supplement, in the light of the circumstances under which they
                were made) not misleading (provided that such counsel need not
                render any opinion with respect to the financial statements and
                other financial, engineering and statistical data included
                therein), and (C) to the best of such counsel's knowledge, no
                stop order has been issued by the Commission suspending the
                effectiveness of such registration statement and

Page 6 - Warrant to Purchase Shares
<PAGE>

                 no proceedings for the issuance of such a stop order are
                 threatened or contemplated;

          (vi)   furnish to the Prospective Sellers whose intended dispositions
                 are required a blue sky survey in the form and of the substance
                 customarily prepared by counsel for the Company and accepted by
                 sellers of securities in similar offerings, discussing and
                 describing the application provisions of the securities or blue
                 sky laws of each state or jurisdiction in which the Company
                 shall be required, pursuant to Section 6(c)(iv), to register or
                 qualify such intended dispositions of such Warrant Shares, or,
                 in the event counsel for the underwriters in such offering
                 shall be preparing a blue sky survey, cause such counsel to
                 furnish such survey to, and to allow reliance thereon by, such
                 Prospective Sellers;

          (vii)  otherwise use its best efforts to comply with all applicable
                 rules and regulations of the Commission under the Securities
                 Act and the Exchange Act, insofar as they relate to such
                 registration and such registration statement; and

          (viii) use its best efforts to list such Warrant Shares on any
                 securities exchange on which any securities of the Company are
                 then listed or to admit such Warrant Shares for trading in any
                 national market system in which any securities of the Company
                 are then admitted for trading, if the listing or admission of
                 such securities is then permitted under the rules of such
                 exchange or system.

     (c) With respect to the registration by the Company of transfers of Warrant
Shares under the Securities Act pursuant to Section 6(a), the Company shall pay
all expenses incurred by it in complying with this Section 6 (including, without
limitation, all registration and filing fees, printing expenses, blue sky fees
and expenses, costs and expenses of audits, and reasonable fees and
disbursements of counsel for the Company and special counsel designated by
Prospective Sellers owning a majority of the Warrant Shares covered by such
registration, but specifically excluding any underwriting discounts and
allowances that are allocable to the Warrant Shares being sold by, and which
shall be paid by, the Prospective Sellers; provided, however, that if any
registration statement filed with the Commission by the Company under Section
6(a) shall not be declared effective by the Commission, such attempted
registration shall not constitute a registration under this Section 6(c).

     (d) It shall be a condition precedent to the obligations of the Company to
take any action pursuant to this Section 6 that each Prospective Seller, the
transfer of whose Warrant Shares is registered or to be registered under each
such registration, shall furnish to the Company such written information
regarding the securities held by such Prospective Seller as the Company shall
reasonably request and as shall be required in connection with the action to be
taken by the Company.

Page 7 - Warrant to Purchase Shares
<PAGE>

     (e)  (i)  In the event of any registration of any transfer of Warrant
Shares under the Securities Act pursuant to this Section 6, the Company will
indemnify and hold harmless each Prospective Seller of such securities, each of
its officers, directors and partners, and each other person, if any, who
controls such Prospective Seller within the meaning of the Securities Act, and
each underwriter, if any, who participates in the offering of such securities,
against any losses, claims, damages or liabilities (or actions in respect
thereof), joint or several, to which each Prospective Seller, officer, director
or partner, controlling person or underwriter may become subject under the
Securities Act or otherwise, insofar as such losses, claims, damages or
liabilities (or actions in respect thereof) arise out of or are based upon any
untrue statement or alleged untrue statement of any material fact contained, on
the effective date thereof, in any registration statement under which such
transfer of securities was registered under the Securities Act, any preliminary
prospectus or final prospectus contained therein, or any amendment or supplement
thereto, or arise out of or are based upon the omission or alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein not misleading, or any violation by the Company of the
Securities Act, and will reimburse such Prospective Seller and each of its
officers, directors and partners, and each such controlling person or
underwriter, for any legal or any other expenses reasonably incurred by such
Prospective Seller or its officers, directors and partners or controlling
persons or by each such underwriter, in connection with investigating or
defending any such loss, claim, damage, liability or action; provided, however,
that the Company will not be liable in any such case to the extent that any such
loss, claim, damage or liability arises out of or is based upon an untrue
statement or alleged untrue statement or omission or alleged omission made in
such registration statement, preliminary prospectus or prospectus or such
amendment or supplement in reliance upon and in conformity with written
information furnished to the Company through an instrument duly executed by such
Prospective Seller specifically for use in the preparation thereof.  In the
event of any registration by the Company or any transfer of securities under the
Securities Act pursuant to this Section 6, each Prospective Seller of Warrant
Shares covered by such registration will indemnify and hold harmless the
Company, each other person, if any, who controls the Company within the meaning
of the Securities Act and each officer and director of the Company and the other
Prospective Sellers to the same extent that the Company agrees to indemnify it,
but only with respect to the written information relating to such Prospective
Seller furnished to the Company by such Prospective Seller aforesaid.

          (ii) Each indemnified party shall, as promptly as practicable upon
receipt of notice of the commencement of any action against such indemnified
party or its officers, directors or partners, or any controlling person of such
indemnified party, in respect of which indemnity may be sought from an
indemnifying party on account of the indemnity agreement contained in Section
6(e)(i), notify the indemnifying party in writing of the commencement thereof.
The omission of such indemnified party to so notify the indemnifying party of
any such action shall not relieve the indemnifying party from any liability
which it may have on account of the indemnity agreement contained in Section
6(e)(i) to the extent that the failure to receive such notice within a
reasonable period of time shall not have caused harm, loss or damage to the
indemnifying party, provided that, conversely, if such failure to receive notice
shall have caused any harm, loss or damage to the

Page 8 - Warrant to Purchase Shares
<PAGE>

indemnifying party, such failure shall constitute a defense to any liability
which such indemnifying party may have on account of such agreement to the
extent of the harm, loss or damage so caused. In case any such action shall be
brought against any indemnified party, its officers, directors and partners, or
any such controlling person, and such indemnified party shall notify the
indemnifying party of the commencement thereof, the indemnifying party shall be
entitled to participate in (and, to the extent that the indemnifying party shall
wish, to direct) the defense thereof at the indemnifying party's own expense, in
which event the defense shall be conducted by recognized counsel chosen by the
indemnifying party and approved by the indemnified party (whose approval shall
not unreasonably be withheld) and the indemnified party may participate in such
defense at its own expense (unless it is advised by counsel that actual or
potential differing interests or defenses exist or may exist, in which case such
expenses shall be paid by the indemnifying party, provided that the indemnifying
party shall not be required to pay the expenses for more than one counsel for
all such indemnified parties).

     7.  TRANSFER; OWNERSHIP.  Subject to Section 5, this Warrant and all rights
hereunder are transferable, in whole or in part, at the office or agency of the
Company referred to in Section 1 by the holder hereof in person or by a duly
authorized attorney, upon surrender of this Warrant, with an assignment,
acceptable to the Company, duly completed, at which time a new Warrant shall be
made and delivered by the Company, of the same tenor as this Warrant but
registered in the name of the transferee.  The holder of this Warrant, by taking
or holding the same, consents and agrees that this Warrant, when endorsed in
blank, shall be deemed negotiable, and that the holder hereof, when this Warrant
shall have been so endorsed, may be treated by the Company and all other persons
dealing with this Warrant as the absolute owner hereof for any purpose and as
the person entitled to exercise the rights represented by this Warrant and to
transfer this Warrant on the books of the Company, any notice to the contrary
notwithstanding; but until such transfer on such books, the Company may treat
the registered holder hereof as the owner hereof for all purposes.  Any transfer
of this Warrant shall be made in compliance with the Securities Act and any
applicable statute securities or blue sky laws.

     8.  EXCHANGE AND REPLACEMENT.  Subject to Section 7, this Warrant is
exchangeable, upon the surrender hereof by the holder hereof at the office or
agency of the Company referred to in Section 1, for new Warrants of like tenor
and date representing in the aggregate the right to purchase the number of
Shares which may be purchased hereunder, each of such new Warrants to represent
the right to purchase such number of Shares as shall be designated by said
holder hereof at the time of such surrender.  Upon receipt by the Company at the
office or agency referred to in Section 1 of evidence reasonably satisfactory to
it of the loss, theft or destruction of this Warrant and of indemnity or
security reasonably satisfactory to it (provided that the written indemnity of
the holder hereof shall be deemed reasonably satisfactory to the Company for
such purposes), the Company will deliver a new Warrant of like tenor and date in
replacement of this Warrant.  This Warrant shall be promptly canceled by the
Company upon the surrender hereof in connection with any transfer, exchange or
replacement.  The Company will pay all expenses and charges payable in
connection with the preparation, execution and delivery of Warrants pursuant to
Section 7 and this Section 8.

Page 9 - Warrant to Purchase Shares
<PAGE>

     9.  NOTICES.  Any notice or other document required or permitted to be
given or delivered to the holder hereof shall be delivered at, or sent by
certified or registered mail to, Level 5, 359 Queen Street, Brisbane,
Queensland, Australia, or to such other address as shall have been furnished to
the Company in writing by the holder hereof.  Any notice or other document
required or permitted to be given or delivered to the Company shall be delivered
at, or sent by certified or registered mail to, 633 Seventeenth Street, Suite
1550, Denver, Colorado 80202, or to such other address as shall have been
furnished in writing to the holder hereof by the Company.  Any notice so
addressed and mailed by registered or certified mail or otherwise delivered,
shall be deemed to be given when actually received by the addressee.

     10.  GOVERNING LAW.  THIS WARRANT SHALL BE GOVERNED BY, AND CONSTRUED AND
ENFORCED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS.

     11.  MISCELLANEOUS.  This Warrant will be binding upon any entity
succeeding to the Company by consolidation or acquisition of all or
substantially all of the Company's assets, and upon any successor or assign of
the holder hereto.  This Warrant and any provision hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party (or any predecessor in interest thereof) against whom enforcement of the
same is sought.  The headings in this Warrant are for purposes of reference only
and shall not affect the meaning or construction of any of the provisions
hereon.

     IN WITNESS WHEREOF, Tipperary Corporation has caused this Warrant to be
signed by its duly authorized officers, under its corporate seal, to be dated
March 8, 2002.

                              TIPPERARY CORPORATION


                              BY:         /s/ David L. Bradshaw
                                      -----------------------------------------
                                ITS:            President
                                      -----------------------------------------

(CORPORATE SEAL)

ATTEST:    /s/ Elaine R. Treece
        -------------------------
   ITS:    Secretary

Page 10 - Warrant to Purchase Shares
<PAGE>

                                                            Annex 1

                             TIPPERARY CORPORATION

                         PROVISIONS AS TO ADJUSTMENT OF
                      EXERCISE PRICE AND NUMBER OF SHARES
                    ISSUED UPON OCCURRENCE OF CERTAIN EVENTS

     The Exercise Price and the number of Shares issuable upon the exercise of
the annexed Warrant to purchase shares of TIPPERARY CORPORATION, a Texas
corporation (herein and in this Warrant referred to as the "Company"), shall be
subject to adjustment from time to time as hereinafter provided; that in no
event shall the Exercise Price be increased to a price greater than One Dollar
and 65/100 ($1.65) U.S. per Share, except as provided by paragraph (C).  Upon
each adjustment of the Exercise Price, the holder of this Warrant shall
thereafter be entitled to purchase, at the Exercise Price resulting from such
adjustment, the number of Shares obtained by multiplying the number of Shares
purchasable pursuant hereto immediately prior to such adjustment by a fraction,
the numerator of which is the Exercise Price in effect immediately prior to such
adjustment and the denominator of which is the Exercise Price resulting from
such adjustment.  In making the adjustments to the Exercise Price and the number
of Shares issuable upon the exercise of this Warrant, the following provisions
shall be applicable:

     (A) If and whenever the Company shall issue or sell any Shares for
consideration per Share that is less than the Exercise Price in effect
immediately prior to the time of such issue or sale at less than the Market
Price (as hereinafter defined) of such Shares on the date of such issue or sale,
then forthwith upon such issue or sale the Exercise Price in effect immediately
prior thereto shall be adjusted to an amount (calculated to the nearest cent)
determined by dividing (i) an amount equal to the sum of (a) the number of
Shares outstanding immediately prior to such issue or sale multiplied by the
Exercise Price in effect immediately prior to such issue or sale, and (b) the
consideration, if any, received by the Company upon such issue or sale by (ii)
the total number of Shares outstanding immediately after such issue or sale;
provided, however, that no adjustment shall be made hereunder by reason of:

          (i) the grant of this Warrant or the issuance of Shares upon the
              exercise of this Warrant or any other outstanding Warrant;

          (ii) the grant by the Company of options to purchase shares in
               connection with any purchase or option plan for the benefit of
               employees of the Company, or any affiliates or subsidiaries
               thereof; or

          (iii) the issuance (whether directly or by assumption in a merger or
                otherwise) or sale (including any issuance or sale to holders of
                Shares) of any securities convertible into or exchangeable for
                Shares (such convertible or exchangeable securities are herein
                referred to as "Convertible Securities"), or the grant of
<PAGE>

                rights to subscribe for or to purchase, or of options for the
                purchase of (including any grant of such rights or options to
                holders of shares, other than pursuant to a dividend on Shares),
                Shares of Convertible Securities, regardless of whether the
                right to convert or exchange such Convertible Securities or such
                rights or options are immediately exercisable.

No adjustment of the Exercise Price shall be required to be made by the Company
and no notice hereunder must be given if the amount of any required adjustment
is less than 5% of the Exercise Price.  In such case any such adjustment shall
be carried forward and shall be made (and notice thereof shall be given
hereunder) at the time of and together with the next subsequent adjustment
which, together with any adjustment so carried forward, shall amount to not less
than 5% of the Exercise Price.

     (B) For the purposes of paragraph (A), the following provisions (i) through
(vi), inclusive, shall also be applicable:

            (i) If, at the time Shares are issued and sold upon the conversion
                or exchange of Convertible Securities or upon the exercise of
                rights or options previously granted by the Company, the price
                per Share for which such Shares are issued (determined by
                dividing (a) the total amount, if any, received by the Company
                as consideration for such Convertible Securities or for the
                granting of such rights or options, plus the aggregate amount of
                additional consideration paid to the Company upon the conversion
                or exchange of such Convertible Securities (which, if so
                provided in such Convertible Securities, shall be deemed to be
                equal to the outstanding principal amount of the indebtedness
                represented by such Convertible Securities) or upon the exercise
                of such rights or options, by (b) the total number of Shares
                issued upon the conversion or exchange of such Convertible
                Securities or upon the exercise of such rights or options) shall
                be less than the Exercise Price in effect immediately prior to
                such issue, sale or exercise, then the adjustments provided for
                by the first paragraph of this Annex 1 and paragraph (A) shall
                be made. In making the adjustment of the Exercise Price provided
                for by paragraph (A), the amount described in clause (a) of this
                paragraph (B)(i) shall be considered the consideration received
                by the Company upon the issue or sale of the Shares for purposes
                of clause (i)(b) of paragraph (A).

          (ii)  In case at any time any Shares or Convertible Securities or any
                rights or options to purchase any Shares or Convertible
                Securities shall be issued or sold for cash, the consideration
                received therefor shall be deemed to be the amount received by
                the Company therefor without deduction therefrom of any expenses
                incurred or any underwriting commissions or concessions paid or
                allowed by the Company in connection therewith. In case any
                Shares or Convertible

Page 2 - Annex 1
<PAGE>

                Securities or any rights or options to purchase any Shares or
                Convertible Securities shall be issued or sold, in whole or in
                part, for consideration other than cash, the amount of the
                consideration other than cash received by the Company in
                exchange for the issue or sale of such Convertible Securities
                shall be deemed to be the fair value of such consideration as
                determined in good faith by the Board of Directors of the
                Company, without deduction therefrom of any expenses incurred or
                any underwriting commissions or concessions paid or allowed by
                the Company in connection therewith; provided that if the holder
                or holders of at least 66-2/3% of the Warrant Shares purchasable
                under this Warrant shall request in writing, the value of such
                consideration shall be determined by an independent expert
                selected by such holders, the costs and expenses of which shall
                be borne by the Company, and, if the value of such consideration
                as so determined is less than the value determined by the Board
                of Directors of the Company, the lesser value shall be utilized
                in calculating the consideration per Share received by the
                Company for purposes of making the adjustment provided by
                paragraph (A). In the event of any merger or consolidation of
                the Company in which the Company is not the surviving
                corporation or in the event of any sale of all or substantially
                all of the assets of the Company for stock or other securities
                of any corporation, the Company shall be deemed to have issued a
                number of Shares for stock or securities of such other
                corporation computed on the basis of the actual exchange ratio
                on which the transaction was predicated and for consideration
                that is equal to the fair market value on the date of such
                transaction of such stock or securities of the other
                corporation, and if any such calculation results in adjustment
                of the Exercise Price, the determination of the number of Shares
                issuable upon exercise of this Warrant immediately prior to such
                merger, consolidation or sale, for purposes of paragraph (A),
                shall be made after giving effect to such adjustment of the
                Exercise Price.

          (iii) The number of Shares outstanding at any given time shall not
                include Shares that have been redeemed by the Company and not
                canceled, if any, and that are thus owned or held by or for the
                account of the Company, and the disposition of any such Shares
                shall be considered an issue or sale of Shares for purposes of
                paragraph (A).

          (iv)  "Market Price" shall mean the lower of (a) the average closing
                sales prices of Shares recorded on the principal national
                securities exchange on which the Shares are listed or in a
                national market system for securities in which the Shares are
                admitted to trading or (b) the average of the closing bid and
                asked prices of Shares reported in the domestic over-the-counter
                market, for the 20 trading days immediately prior to the day as
                of which the Market Price is being determined. If the Shares are
                not listed on any national securities exchange or

Page 3 - Annex 1
<PAGE>

               admitted for trading in any national market system or traded in
               the domestic over-the-counter market, the Market Price shall be
               the higher of (y) the book value of the Shares as determined by a
               firm of independent public accountants of recognized standing
               selected by the Board of Directors of the Company as of the last
               day of any month ending within 60 days preceding the date as of
               which the determination is to be made or (z) the fair market
               value of the Shares determined in good faith by the Board of
               Directors of the Company, provided that if the holder or holders
               of at least 66-2/3% of the Warrant Shares purchasable under the
               Warrant shall request in writing, the fair market value of the
               Shares shall be determined by an independent investment banking
               firm or other independent expert selected by such holders and
               reasonably satisfactory to the Company, which determination shall
               be as of a date which is within 15 days of the date as of which
               the determination is to be made.

          (v)  Anything herein to the contrary notwithstanding, in case the
               Company shall issue any Shares in connection with the acquisition
               by the Company of the stock or assets of any other corporation or
               the merger of any other corporation into the Company under
               circumstances where, on the date of the issuance of such Shares,
               the consideration received for such Shares is less than the
               Market Price of the Shares, but on the date the number of Shares
               was determined, the consideration received for such Shares would
               not have been less than the Market Price thereof, such Shares
               shall not be deemed to have been issued for less than the Market
               Price.

          (vi) Anything in clause (ii) of this paragraph (B) to the contrary
               notwithstanding, in the case of an acquisition where all or part
               of the purchase price is payable in Shares or Convertible
               Securities but is stated as a dollar amount, where the Company
               upon making the acquisition pays only part of a maximum dollar
               purchase price which is payable in Shares or Convertible
               Securities and where the balance of such purchase price is
               deferred or is contingently payable under a formula related to
               earnings over a period of time, (a) the consideration received
               for any Shares or Convertible Securities delivered at the time of
               the acquisition shall be deemed to be such part of the total
               consideration as the portion of the dollar purchase price then
               paid in Shares or Convertible Securities bears to the total
               maximum dollar purchase price payable in Shares or Convertible
               Securities and (b) in connection with each issuance of additional
               Shares or Convertible Securities pursuant to the terms of the
               agreement relating to such acquisition, the consideration
               received shall be deemed to be such part of the total
               consideration as the portion of the dollar purchase price then
               and theretofore paid in Shares or Convertible Shares bears to the
               total maximum dollar purchase price payable in Shares or
               Convertible Securities multiplied by a fraction, the numerator of
               which shall be the number of Shares (or in the case

Page 4 - Annex 1
<PAGE>

               of Convertible Securities other than capital stock of the
               Company, the aggregate principal amount of such Convertible
               Securities) then issued and the denominator of which shall be the
               total number of shares (or in the case of Convertible Securities
               other than capital stock of the Company, the aggregate principal
               amount of such Convertible Securities) then and theretofore
               issued under such acquisition agreement. In the event only a part
               of the purchase price for an acquisition is paid in Shares or
               Convertible Securities in the manner referred to in this clause
               (vi), the term "total consideration" as used in this clause (vi)
               shall mean that part of the aggregate consideration as is fairly
               allocable to the purchase price paid in Shares or Convertible
               Securities in the manner referred to in this clause (vi), as
               determined by the Board of Directors of the Company.

     (C) In the case at any time the Company shall subdivide its outstanding
Shares into a greater number of Shares, then from and after the record date for
such subdivision the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced and the number of Shares
purchasable upon the exercise of this Warrant shall be correspondingly
increased, and, conversely, in case the outstanding Shares shall be combined
into a smaller number of Shares, then from and after the record date for such
combination the Exercise Price in effect immediately prior to such combination
shall be proportionately increased and the number of Shares purchasable upon the
exercise of this Warrant shall be correspondingly decreased.

     (D) Unless the provisions of paragraph (E) apply, if any capital
reorganization or reclassification of the capital stock of the Company, or
consolidation or merger of the Company with another corporation, or sale of all
or substantially all of its assets to another corporation, shall be effected in
such a way that holders of Shares (or any other securities of the Company then
issuable upon the exercise of this Warrant) shall be entitled to receive stock,
securities or assets with respect to or exchange for Shares (or such other
securities) then, as a condition of such reorganization, reclassification,
consolidation, merger or sale, lawful and adequate provision shall be made
whereby the holder hereof shall thereafter have the right to purchase and
receive upon the basis and upon the terms and conditions specified in this
Warrant and in lieu of the Shares (or other securities) of the Company
immediately theretofore purchasable and receivable upon the exercise of the
rights represented hereby, such shares of stock, securities or assets as may be
issued or payable with respect to or in exchange for a number of outstanding
Shares (or other securities) equal to the number of Shares (or other securities)
immediately theretofore so purchasable and receivable had such reorganization,
reclassification, consolidation, merger or sale not taken place, and in any such
case appropriate provision shall be made with respect to the rights and
interests of the holder of this Warrant to the end that the provisions hereof
(including, without limitation, provisions for adjustment of the Exercise Price
and of the number of Shares (or other securities) purchasable upon the exercise
of this Warrant and for the registration thereof as provided in Section 6 of
this Warrant) shall thereafter be applicable, as nearly as may be, in relation
to any shares of stock, securities or assets thereafter deliverable upon the
exercise hereof (including an immediate adjustment, by reason

Page 5 - Annex 1
<PAGE>

of such consolidation, merger or sale, of the Exercise Price to the value of the
Shares (or other securities) reflected by the terms of such consolidation,
merger or sale if the value so reflected is less than the Exercise Price in
effect immediately prior to such consolidation, merger or sale). In the event of
a consolidation or merger of the Company with or into another corporation as a
result of which a greater or lesser number of securities of the surviving
corporation are issuable to holders of Shares in respect of the number of Shares
outstanding immediately prior to such consolidation or merger, then the Exercise
Price in effect immediately prior to such consolidation or merger shall be
adjusted in the same manner as though there were a subdivision or combination of
the outstanding Shares. The Company shall not effect any such consolidation,
merger or sale, unless prior to or simultaneously with the consummation thereof
the surviving or successor corporation (if other than the Company) resulting
from such consolidation or merger of the corporation purchasing such assets
shall assume, by written instrument executed and mailed to the registered holder
hereof at the last address of such holder appearing on the books of the Company,
the obligation to deliver to such holder such Shares of stock, securities or
assets as, in accordance with the foregoing provisions, such holder may be
entitled to purchase, and containing the express assumption of such surviving or
successor corporation of the due performance of every provision of this Warrant
to be performed by the Company and of all liabilities and obligations of the
Company hereunder.

     (E) In the event of a change in control of the Company, as defined in this
paragraph (E), then the Board of Directors shall accelerate the exercise date of
the Warrant or make this Warrant fully vested and exercisable and, in its sole
discretion, may take any or all of the following actions: (a) grant a cash bonus
award to any holder of this Warrant in an amount necessary to pay the Exercise
Price of all or any portion of the Warrant then held by such person; (b) pay
cash to any holder of this Warrant in exchange for the cancellation of the
holder's Warrant in an amount equal to the difference between the Exercise Price
of such Warrant and the greater of the tender offer price for the underlying
Shares or the Market Price of the Shares on the date of the cancellation of the
Warrant; and (c) make any other adjustments or amendments to this Warrant.  For
purposes of this paragraph (E), a "change in control" shall be deemed to have
occurred if (a) any "person" or "group" (within the meaning of Sections 13(d)
and 14(d)(2) of the Securities Exchange Act of 1934, as amended ("1934 Act"),
other than a trustee or other fiduciary holding securities under an employee
benefit plan of the Company is or becomes the "beneficial owner" (as defined in
Rule 13d-3 under the 1934 Act), directly or indirectly, of more than 50% of the
then outstanding voting stock of the Company; or (b) at any time during any
period of three consecutive years after the date of this Warrant, individuals
who at the beginning of such period constitute the Board (and any new director
whose election by the Board or whose nomination for election by the Company's
stockholders was approved by a vote of at least two-thirds of the directors then
still in office who either were directors at the beginning of such period or
whose election or nomination for election was previously so approved) cease for
any reason to constitute a majority thereof; or (c) the stockholders of the
Company approve a merger or consolidation of the Company with any other
corporation, other than a merger or consolidation which would result in the
voting securities of the Company outstanding immediately prior thereto
continuing to represent (either by remaining outstanding or by being converted
into voting securities of the surviving entity) at least 50% of the combined
voting power of

Page 6 - Annex 1
<PAGE>

the voting securities of the Company or such surviving entity outstanding
immediately after such merger or consolidation.

     (F) In case at any time the Company shall pay any dividend on or make any
other distribution with respect to Shares (or any other securities of the
Company then issuable upon the exercise of the Warrant) that is payable in
Shares, Convertible Securities, any other securities of the Company or other
stock, securities or assets, other than cash, then thereafter, and in lieu of
any adjustment of the Exercise Price and the number of Shares issuable upon the
exercise of this Warrant, the holder of this Warrant, upon any exercise of the
rights represented hereby, shall be entitled to receive the number of Shares (or
other securities) being purchased upon such exercise and, in addition to and
without further payment, the Shares, Convertible Securities, other securities of
any company or other stock, securities or assets which the holder of this
Warrant would have received by way of such distributions if continuously since
the date of the Warrant (or, if this Warrant shall have been issued pursuant to
Section 7 of this Warrant, the date of the predecessor Warrant to which this
Warrant relates) such holder had been the record holder of the number of Shares
(or other securities), then being purchased and had retained all such Shares,
Convertible Securities, other securities of the Company or other stock,
securities or assets distributable with respect to such Shares (or other
securities) and, furthermore, all cash, stock, securities or assets payable as
dividends or distributions with respect to the foregoing and originating
directly or indirectly therefrom.  The Company shall reserve and retain in
escrow from any such dividend or distribution of Shares, Convertible Securities,
other securities of the Company or other stock, securities or assets, and from
any such dividends or distributions with respect thereto and originating
directly or indirectly therefrom, such Shares, Convertible Securities, other
securities of the Company and other stock, securities, assets and cash as shall
be necessary to fulfill its obligations to the holder hereof pursuant to this
paragraph (F).

     (G) If at any time conditions arise by reason of action taken by the
Company, which in the good faith opinion of the Board of Directors of the
Company, are not adequately covered by the provisions of this Annex 1, and which
might materially adversely affect the rights of the holder of this Warrant, the
Company shall appoint a firm of independent public accountants of recognized
standing (which may be the regular accountants or auditors of the Company),
which shall give their opinion as to the adjustments, if any, in the Exercise
Price and the number of Shares purchasable upon the exercise of this Warrant, or
other change in the rights of the holder hereof, on a basis consistent with the
other provisions of this Annex 1, necessary to preserve without diminution the
rights of the holder hereof.  Upon receipt of such opinion, the Company shall
forthwith make the adjustments described therein.

     (H)  (i)  Within ten (10) days of any adjustment of the Exercise Price or
              change in the number of Shares purchasable upon the exercise of
              this Warrant made pursuant to paragraphs (A), (B), (C), or (F) or
              any change in the rights of the holder of this Warrant by reason
              of the occurrence of events described in paragraphs (D), (E), or
              (F), the Company shall give written notice by certified or
              registered mail to the registered holder of this Warrant at the
              address of such holder as shown on the books of the Company, which
              notice shall describe the event requiring

Page 7 - Annex 1
<PAGE>

              such adjustments (with respect to any adjustment made pursuant to
              paragraphs (C), (D), (E) or (F), the Exercise Price resulting from
              such adjustment, the increase or decrease, if any, in the number
              of Shares purchasable upon the exercise of this Warrant, or the
              other change in the rights of such holder, and set forth in
              reasonable detail the method of calculation of such adjustments
              and the facts upon which such calculations are based. Within two
              (2) days of receipt from the holder of this Warrant upon the
              surrender hereof for exercise pursuant to Section 1 of this
              Warrant, and within three (3) days of receipt from the holder
              hereof a written request therefor (which request shall not be made
              more than once each calendar quarter), the Company shall give
              written notice by certified or registered mail to such holder at
              his address as shown on the books of the Company of the Exercise
              Price in effect as of the date of receipt by the Company of this
              Warrant for exercise, or the date of receipt of such written
              request, and the number of Shares purchasable or the number or
              amount of other shares of stock, securities or assets receivable
              as of such date, and set forth in reasonable detail the method of
              calculation of such numbers; provided that no further adjustments
              to the Exercise Price or the number of Shares purchasable or
              number or amount of shares, securities or assets receivable on
              exercise of this Warrant shall be made after receipt of this
              Warrant by the Company for exercise.

         (ii) Upon each adjustment of the Exercise Price and each change in the
              number of Shares purchasable upon the exercise of this Warrant,
              and change in the rights of the holder of this Warrant by reason
              of the occurrence of other events herein set forth, then and in
              each case, upon written request of the holder of this Warrant
              (which request shall be made not more often than once each
              calendar year), the Company will at its expense promptly obtain an
              opinion of independent public accountants reasonably satisfactory
              to each holder stating the then effective Exercise Price and the
              number of Shares then purchasable, or specifying the other shares
              of stock, securities or assets and the amount thereof then
              receivable, and setting forth in reasonable detail the method of
              calculation of such numbers and the facts upon which such
              calculations are based.  The Company will promptly mail a copy of
              such opinion to the registered holder hereof.

     (I)  In case at any time:

          (i) The Company shall pay any dividend payable in capital stock on
              its outstanding Shares or make any distribution (other than
              regular cash dividends) to the holders of Shares;

         (ii) The Company shall offer for subscription pro rata to the holders
              of Shares any additional capital stock or other rights;

Page 8 - Annex 1
<PAGE>

           (iii) There shall be authorized any capital reorganization or
                 reclassification of the capital stock of the Company, or
                 consolidation or merger of the Company with, or sale of all or
                 substantially all of its assets to, another corporation; or

           (iv)  There shall be authorized or commence a voluntary or
                 involuntary dissolution, liquidation or winding up of the
                 Company.

then, in one or more of said cases, the Company shall given written notice by
certified or registered mail to Barber at the address of Barber as shown on the
books of the Company on the date on which (1) the books of the Company shall
close or a record shall be taken for such dividend, distribution, or
subscription rights, or (2) such reorganization, reclassification,
consolidation, merger, sale, dissolution, liquidation or winding up shall take
place or be voted upon by the shareholders of the Company, as the case may be.
Such notice shall also specify the date as of which the holders of record of
Shares shall participate in such dividend, distribution or subscription rights,
or shall be entitled to exchange their Shares for securities or other property
deliverable upon such reorganization, reclassification, consolidation, merger,
sale, dissolution, liquidation or winding up, as the case may be.  Such written
notice shall be given at least thirty (30) days prior to the action in question
and no less than thirty (30) days prior to the record date or the date on which
the Company's books are closed in respect thereto.

Page 9 - Annex 1
<PAGE>

EXHIBIT A

                               SUBSCRIPTION FORM

                    To be Executed by the Registered Holder
                  Desiring to Exercise the Within Warrant of
                             TIPPERARY CORPORATION


     The undersigned registered holder hereby exercises the right to purchase
__________________________ Shares covered by the within Warrant according to the
conditions thereof, and herewith makes payment of the Exercise Price of such
Shares, $ _____________________.


Name of Registered Holder:

---------------------------------------

Signature:

---------------------------------------

Title of Signing Officer
or Agent (if any):

---------------------------------------

Address of Registered Holder:

---------------------------------------

Tax I.D. No.:

---------------------------------------

Dated:  ____________________, 20_______.